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Showing $\sum_{i=1}^nq_i\sqrt{p_i}+q_0$ is irrational for $q_0,...,q_n\in\mathbb{Q}$, $q_1,...,q_n\not=0$, and $p_i$ distinct prime
In my analysis class these questions have kept coming up over and over again about sums of radicals of primes being irrational. I wanted to just prove the general case so I never had to worry again. ...
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6
votes
1
answer
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Number of real roots of a separable real polynomial doesn't change under small perturbations
Say we have a polynomial with real coefficients and no repeated roots. Knowing that the roots of a polynomial vary continuously in the coefficients (so long as we don't change the degree), it seems ...
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